calculate pH of the buffer solution prepared by mixing 10 mL of 1.5 M HCl with 100 mL of 0.1 M K2CO3 solution. For H2CO3: Ka1= 4.46 e^-7, Ka2= 4.69e^-11
pH = pKa + log(B/A)
mols K2CO3 = M x L.
mols HCl = M x L.
Calculate mols K2CO3 initially.
Calculate mols HCl initially.
I think you will find that one H ion has been added to the CO3^=, and you are half way between CO3^= and H2CO3 meaning that CO3^= and H2CO3 are the same.
Therefore, log B/A = log 1 = 0 and pH = pKa1.
Post any work if you have questions.
To calculate the pH of the buffer solution, we need to determine the concentrations of the conjugate acid (H2CO3) and the conjugate base (CO3^2-) in the solution.
Let's start by finding the moles of HCl and K2CO3 in the solution:
Moles of HCl = volume (in L) × concentration
= 10 mL × (1.5 M / 1000 mL/L)
= 0.015 moles
Moles of K2CO3 = volume (in L) × concentration
= 100 mL × (0.1 M / 1000 mL/L)
= 0.01 moles
Next, we need to determine the moles of H2CO3 and CO3^2- produced when HCl and K2CO3 react.
Since HCl is a strong acid and K2CO3 is a strong base, they will react completely to form H2CO3 and KCl:
HCl + K2CO3 → H2CO3 + 2KCl
This means that the moles of H2CO3 and CO3^2- produced will be equal to the moles of HCl and K2CO3 used in the reaction.
Therefore, the moles of H2CO3 and CO3^2- in the solution would also be 0.015 moles and 0.01 moles, respectively.
Now, let's calculate the concentrations of H2CO3 and CO3^2- in the solution:
Concentration of H2CO3 = moles / volume (in L)
= 0.015 moles / (10 mL + 100 mL) / 1000 mL/L
= 0.015 M
Concentration of CO3^2- = moles / volume (in L)
= 0.01 moles / (10 mL + 100 mL) / 1000 mL/L
= 0.01 M
Since H2CO3 is a weak acid with two dissociation constants (Ka1 and Ka2), we need to consider both of them while calculating the pH of the buffer solution.
The pH of the buffer solution can be found using the Henderson-Hasselbalch equation:
pH = pKa + log [base] / [acid]
For the first dissociation of H2CO3 (Ka1 = 4.46 × 10^-7):
pKa1 = -log (Ka1)
= -log (4.46 × 10^-7)
= 6.35
Now, let's calculate the pH using the Henderson-Hasselbalch equation with the first dissociation:
pH = 6.35 + log (0.01 M / 0.015 M)
Finally, plug in the values and solve for pH:
pH = 6.35 + log (0.667)
Using a calculator, we find that log (0.667) ≈ -0.174.
Therefore, the pH of the buffer solution is approximately:
pH ≈ 6.35 + (-0.174)
≈ 6.18
So, the pH of the buffer solution is approximately 6.18.